The Argentine World Player of the Year struck twice in 12 first-half minutes and again in the 79th to move two goals clear of Real forward Cristiano Ronaldo at the top of the La Liga scoring charts with 24 goals.
The victory lifted the champions to 61 points from 22 matches and beat the previous best for straight league wins set by Alfredo Di Stefano's Real in the 1960/61 season.
Villarreal earlier squandered a chance to close within three points of Real and lost their unbeaten home record when they slumped to a 1-0 defeat against promoted Levante.
Athletic Bilbao boosted their chances of a place in Europe when goals from David Lopez, Gaizka Toquero and Fernando Llorente gave them a 3-0 home win over 10-man Sporting Gijon.
The victory lifted the Basque club to fifth place on 38 points, a point above Espanyol who were three goals down by the 18th minute at Almeria and eventually lost 3-2.
MESSI MAGIC
Atletico were looking for a morale-boosting result at the Nou Camp that would keep their hopes of European qualification alive but any prospects of derailing the Barca express were effectively snuffed out by two moments of Messi magic.
His first goal in the 17th minute was a trademark dash in from the right wing and he left several opponents trailing before arrowing a low shot past David De Gea.
Spain striker David Villa slipped the ball through for Messi to score his second in the 29th. Atletico captain Antonio Lopez got a foot to the ball but Messi burst clear and clipped a shot in off the right-hand post from close-range.
The 23-year-old had a powerful header acrobatically saved by De Gea before he beat Diego Godin to a loose ball and prodded it over the line to complete a memorable treble.
"I am happy with the win against a tough team who are not going through the best time and that could have made things hard for us," Messi told Spanish television.
"I am not thinking about being league top scorer at all," he added. "The important thing is that we continue this winning run as we have Real Madrid just behind us and we know they will fight to the end."
Atletico are seventh on 30 points, seven behind Espanyol and eight adrift of Bilbao.
In other games on Saturday, Getafe thumped visiting Deportivo La Coruna 4-1 and Real Mallorca were held to a 1-1 draw at Osasuna as Japanese midfielder Akihiro Ienaga made his debut for the Balearic Islands club.
Real Zaragoza and visitors Racing Santander played out a 1-1 stalemate.
